dgglse(3P) Sun Performance Library dgglse(3P)NAMEdgglse - solve the linear equality-constrained least squares (LSE)
problem
SYNOPSIS
SUBROUTINE DGGLSE(M, N, P, A, LDA, B, LDB, C, D, X, WORK, LDWORK,
INFO)
INTEGER M, N, P, LDA, LDB, LDWORK, INFO
DOUBLE PRECISION A(LDA,*), B(LDB,*), C(*), D(*), X(*), WORK(*)
SUBROUTINE DGGLSE_64(M, N, P, A, LDA, B, LDB, C, D, X, WORK, LDWORK,
INFO)
INTEGER*8 M, N, P, LDA, LDB, LDWORK, INFO
DOUBLE PRECISION A(LDA,*), B(LDB,*), C(*), D(*), X(*), WORK(*)
F95 INTERFACE
SUBROUTINE GGLSE([M], [N], [P], A, [LDA], B, [LDB], C, D, X, [WORK],
[LDWORK], [INFO])
INTEGER :: M, N, P, LDA, LDB, LDWORK, INFO
REAL(8), DIMENSION(:) :: C, D, X, WORK
REAL(8), DIMENSION(:,:) :: A, B
SUBROUTINE GGLSE_64([M], [N], [P], A, [LDA], B, [LDB], C, D, X, [WORK],
[LDWORK], [INFO])
INTEGER(8) :: M, N, P, LDA, LDB, LDWORK, INFO
REAL(8), DIMENSION(:) :: C, D, X, WORK
REAL(8), DIMENSION(:,:) :: A, B
C INTERFACE
#include <sunperf.h>
void dgglse(int m, int n, int p, double *a, int lda, double *b, int
ldb, double *c, double *d, double *x, int *info);
void dgglse_64(long m, long n, long p, double *a, long lda, double *b,
long ldb, double *c, double *d, double *x, long *info);
PURPOSEdgglse solves the linear equality-constrained least squares (LSE) prob‐
lem:
minimize || c - A*x ||_2 subject to B*x = d
where A is an M-by-N matrix, B is a P-by-N matrix, c is a given M-vec‐
tor, and d is a given P-vector. It is assumed that
P <= N <= M+P, and
rank(B) = P and rank( ( A ) ) = N.
( ( B ) )
These conditions ensure that the LSE problem has a unique solution,
which is obtained using a GRQ factorization of the matrices B and A.
ARGUMENTS
M (input) The number of rows of the matrix A. M >= 0.
N (input) The number of columns of the matrices A and B. N >= 0.
P (input) The number of rows of the matrix B. 0 <= P <= N <= M+P.
A (input/output)
On entry, the M-by-N matrix A. On exit, A is destroyed.
LDA (input)
The leading dimension of the array A. LDA >= max(1,M).
B (input/output)
On entry, the P-by-N matrix B. On exit, B is destroyed.
LDB (input)
The leading dimension of the array B. LDB >= max(1,P).
C (input/output)
On entry, C contains the right hand side vector for the least
squares part of the LSE problem. On exit, the residual sum
of squares for the solution is given by the sum of squares of
elements N-P+1 to M of vector C.
D (input/output)
On entry, D contains the right hand side vector for the con‐
strained equation. On exit, D is destroyed.
X (output)
On exit, X is the solution of the LSE problem.
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal LDWORK.
LDWORK (input)
The dimension of the array WORK. LDWORK >= max(1,M+N+P). For
optimum performance LDWORK >= P+min(M,N)+max(M,N)*NB, where
NB is an upper bound for the optimal blocksizes for DGEQRF,
DGERQF, DORMQR and DORMRQ.
If LDWORK = -1, then a workspace query is assumed; the rou‐
tine only calculates the optimal size of the WORK array,
returns this value as the first entry of the WORK array, and
no error message related to LDWORK is issued by XERBLA.
INFO (output)
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
6 Mar 2009 dgglse(3P)
